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An integral lift of contact homology

Jo Nelson

Columbia U

Location

University of Pennsylvania

DRL 4C2

Our first of the new semester

Contact geometry is the study of geometric structures on odd dimensional smooth manifolds given by a hyperplane field specified by a one form which satisfies a maximum nondegeneracy condition called complete non-integrability. The associated one form is called a contact form and uniquely determines a vector field called the Reeb vector field on the manifold. I will explain how one to make use of J-holomorphic curves to obtain a Floer theoretic contact invariant whose chain complex is generated by Reeb orbits. In particular, I will explain the pitfalls in defining contact homology and discuss joint work with Hutchings which gives a rigorous construction of cylindrical contact homology via geometric methods. This talk will feature lots of graphics to acclimate people to the realm of contact geometry.

How to get to Penn's Mathematics Department

The Mathematics Department Office is located on the fourth (top) floor of David Rittenhouse Laboratory ("DRL"). The building is at 209 South 33rd Street (the Southeast corner of 33rd. and Walnut Streets). Note 33rd Street runs one way northwhile Walnut runs one waywest.

We are about a 15 minute walk from the main 30th Street Station and 5 minutes from the University City Rail Station at 32nd and Spruce (=South Street & Convention Avenue). Coming from the airport by train (about 15 minutes): the University City Rail Station is the second stop after you leave the airport.

If you drive, the most convenient public parking is in the pay lot whose entrance is on 34th Street between Market and Chestnut Streets.